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Fungrim entry: def588

Symbol: Binomial (nk){n \choose k} Binomial coefficient
Domain Codomain
nZ0  and  kZ0n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0} (nk)Z0{n \choose k} \in \mathbb{Z}_{\ge 0}
nC  and  kZ0n \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0} (nk)C{n \choose k} \in \mathbb{C}
Table data: (P,Q)\left(P, Q\right) such that (P)        (Q)\left(P\right) \;\implies\; \left(Q\right)
Fungrim symbol Notation Short description
Binomial(nk){n \choose k} Binomial coefficient
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
    SymbolDefinition(Binomial, Binomial(n, k), "Binomial coefficient"),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0))), Element(Binomial(n, k), ZZGreaterEqual(0))), Tuple(And(Element(n, CC), Element(k, ZZGreaterEqual(0))), Element(Binomial(n, k), CC)))))

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2021-03-15 19:12:00.328586 UTC